management / line
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management
The person or group of people that leads an organization, department, or project and bears responsibility.
Die neue Leitung des Museums hat viele Veränderungen angekündigt.
The new management of the museum has announced many changes.
'Leitung' is derived from the verb 'leiten' (to lead/conduct). The ending '-ung' makes it a feminine noun. The basic meaning 'to lead' or 'to lead from A to B' connects all meanings: you can lead people, water, or electricity.
Er leitet die Abteilung seit fünf Jahren.
He has headed the department for five years.
You can easily recognize the meaning from context. If it is about people, a company, or a project, it means leadership or management. If it is about water, electricity, gas, or data, it means the physical pipe or cable.
Die Leitung hat eine neue Strategie beschlossen.
Management has decided on a new strategy.
When referring to a leadership position, the phrases 'die Leitung übernehmen' (to take over the leadership/management) or 'die Leitung haben' (to be in charge) are often used.
Wer hat hier die technische Leitung?
Who is in charge of the technical management here?
The idiom 'eine lange Leitung haben' (to be slow on the uptake) or 'auf der Leitung stehen' (to be confused/not get it) means that someone understands something only slowly. It figuratively refers to a poor telephone connection from the past.
Entschuldigung, ich stand gerade auf der Leitung. Kannst du das wiederholen?
Sorry, I just wasn't getting it. Can you repeat that?
The phrase 'unter der Leitung von' (under the direction of) is a fixed expression. 'Von' is always followed by a person or institution in the dative.
Das Projekt steht unter der Leitung von Frau Dr. Meier.
The project is under the direction of Dr. Meier.
connection / association
'Verbindung' and 'Leitung' can both occur in technical contexts. 'Verbindung' describes that communication, data, or electricity is actually going from one side to the other. 'Leitung' usually means the cable or pipe through which electricity, water, gas, or data flows. That is why, for example, you say that the connection is bad when a phone call keeps dropping. But you say that a line or pipe is broken when the cable or pipe is damaged. The words are easy to confuse because a connection often comes through a line. The important point is: 'Leitung' is more the means, while 'Verbindung' is more the contact or the functioning connection.
Nach dem Sturm musste ein Techniker die beschädigte Leitung reparieren.
After the storm, a technician had to repair the damaged line.
Während des Videoanrufs war die Verbindung plötzlich weg.
During the video call, the connection suddenly dropped.